初中数学(1-1/2^2)(1-1/3^2)(1-1/4^2)……*(1-1/100^2)

(1-1/2^2)(1-1/3^2)(1-1/4^2)……*(1-1/100^2)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)……*(1-1/99)(1+1/99)(1-1/100)(1+1/100)
=1/2*3/2*2/3*4/3……*98/99*100/99*99/100*101/100
=1/2*(3/2*2/3*4/3……*98/99*100/99*99/100*)101/100
=1/2*1*101/100
=101/200

(1-1/2^2)(1-1/3^2)(1-1/4^2)···(1-1/n^2)···(1-1/100^2)
=(i=2,100)∏(1-1/i^2)
=(i=2,100)∏[(1+1/i)(1-1/i)]
=(i=2,100)∏(1+1/i)×(i=2,100)∏(1-1/i)
=[(3/2)×(4/3)×(5/4)×···×(101/100)]
×[(1/2)×(2/3)×(3/4)×···×(99/100)]
=(101/2)×(1/100)
=101/200
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